2003/01/31 by Imre Tuba, Hans Wenzl
Mathematics · #math.QA #math.RA #math.RT #msc:20G42 #msc:17B37 #msc:18D10 #msc:20F36 #msc:20C08 #msc:46L37
published as J. Reine Angew. Math., 581, (2005), 31-69 · 31 pages, followed by a 2-page erratum
arxiv created 2020/02/12 · arxiv updated 2020/02/13
We give a full classification of all braided semisimple tensor categories whose Grothendieck semiring is the one of Rep(O(∞) (formally), Rep(O(N), Rep(Sp(N) or of one of its associated fusion categories. If the braiding is not symmetric, they are completely determined by the eigenvalues of a certain braiding morphism, and we determine precisely which values can occur in the various cases. If the category allows a symmetric braiding, it is essentially determined by the dimension of the object corresponding to the vector representation. Note that the paper is followed by a brief erratum, which corrects a mistake, which does not affect the main results of the paper.